Displaying similar documents to “Regarding a question about the least element map”

A Programmatic Note: on two Types of Intertextuality

Reviel Netz (2005)

Revue d'histoire des mathématiques

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The note addresses briefly some reactions to a previous article “”. In particular it looks at the question: if indeed any text must depend on previous texts, what makes the dependency of commentary and commentary-like text so special to justify my emphasis on this form of writing ? A suggestion is developed, trying to define Deuteronomic texts through their precise semiotics of intertextuality: in general, it is argued, intertextuality may be paradigmatic (= allusion) or syntagmatic...

Comments to Prof. French's article (Vol. 4, nr. 1, 1989 of ).

D. D. Biggins, C. M. Forrest, P. Jackson, R. M. Loynes, James T. Townsend, Simon French (1990)

Trabajos de Estadística

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The comments made by various authors to Prof. French's article Statistical and decision theoretic aspects of examination assessment (Trabajos de Estadística, vol. 4, nr. 1, 1989) were not included in the published paper. In order to complete the article, such comments are published now and the author's answer to them is printed again.

Scientific intuition of Genii against mytho-‘logic’ of Cantor’s transfinite ‘paradise’

Alexander A. Zenkin (2005)

Philosophia Scientiae

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In the paper, a detailed analysis of some new logical aspects of Cantor’s diagonal proof of the uncountability of continuum is presented. For the first time, strict formal, axiomatic, and algorithmic definitions of the notions of potential and actual infinities are presented. It is shown that the actualization of infinite sets and sequences used in Cantor’s proof is a , but hidden, condition of the proof. The explication of the necessary condition and its factual usage within the framework...

It’s not that they couldn’t

Reviel Netz (2002)

Revue d'histoire des mathématiques

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The article offers a critique of the notion of ‘concepts’ in the history of mathematics. Authors in the field sometimes assume an argument from conceptual impossibility: that certain authors could not do X because they did not have concept Y. The case of the divide between Greek and modern mathematics is discussed in detail, showing that the argument from conceptual impossibility is empirically as well as theoretically flawed. An alternative account of historical diversity is offered,...

Mathematical practice and naturalist epistemology : structures with potential for interaction

Bart Van Kerkhove, Jean Paul Van Bendegem (2005)

Philosophia Scientiae

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In current philosophical research, there is a rather one-sided focus on the foundations of proof. A full picture of mathematical practice should however additionally involve considerations about various methodological aspects. A number of these is identified, from large-scale to small-scale ones. After that, naturalism, a philosophical school concerned with scientific practice, is looked at, as far as the translations of its epistemic principles to mathematics is concerned. Finally,...